A hierarchical creep model for cement paste: From decoding nano-microscopic C-S-H creep to considering microstructure evolution

The creep of cement paste significantly affects the long-term performance of concrete structures. However, the accurate prediction of cement paste creep remains to meet enormous challenges. This work proposes a hierarchical creep model of cement paste considering the hydration microstructure evolution. First, the microstructural evolutions are quantitatively captured by a cement hydration model. The creep property of cement paste is upscaled from high-density (HD) and low-density (LD) calcium silicate hydrate (C-S-H) at the nanoscale, via C-S-H gels at the sub-micrometer scale to the microscopic scale by coupling the mean-field theory with the transfer function method. The creep behavior of HD and LD C-S-H is described using a fractional Maxwell model in the time domain and its corresponding transfer function in the Laplace-Carson domain. The creep parameters of HD and LD C-S-H are identified through a back-analysis approach. The determined creep parameters and the hierarchical creep model are validated by comparing them with extensive experimental data. Furthermore, the proposed model quantitatively evaluates the influences of various factors on the creeps of cement paste and C-S-H gels. The results indicate that C-S-H gels should not be treated as a phase with stable viscoelastic creep properties, and cement paste creep can be tailored via proper design for these factors.